Ding and Heng in [1]} showed that the subfield code of \(\mathcal {C}\)  can be represented by the following trace form:
\(\begin{split}\mathcal {C}_f=\left\lbrace \left(\left( {\rm Tr}_1^m\left(af(x)+bx\right)+c\right)_{x \in \mathbb {F}_{p^m}}, {\rm Tr}_1^m(a)\right) : \, a,b \in \mathbb {F}_{p^m}, c \in \mathbb {F}_p\right\rbrace .\end{split}\) 
